scholarly journals Universal quantum uncertainty relations: Minimum-uncertainty wave packet depends on measure of spread

2019 ◽  
Vol 383 (16) ◽  
pp. 1850-1855
Author(s):  
Anindita Bera ◽  
Debmalya Das ◽  
Aditi Sen(De) ◽  
Ujjwal Sen
Keyword(s):  
Wave Packet ◽  
Uncertainty Relations ◽  
Quantum Uncertainty ◽  
Universal Quantum ◽  
Minimum Uncertainty

scholarly journals Universal quantum uncertainty relations between nonergodicity and loss of information

2018 ◽  
Vol 97 (3) ◽  
Author(s):  
Natasha Awasthi ◽  
Samyadeb Bhattacharya ◽  
Aditi Sen(De) ◽  
Ujjwal Sen
Keyword(s):  
Uncertainty Relations ◽  
Loss Of Information ◽  
Quantum Uncertainty ◽  
Universal Quantum

The Uncertainty Principle Derived by The Finite Transmission Speed of Light and Information

2014 ◽  
Vol 3 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Piero Chiarelli
Keyword(s):  
Uncertainty Principle ◽  
Large Scale ◽  
Uncertainty Relations ◽  
Speed Of Light ◽  
Energy Fluctuation ◽  
Hydrodynamic Analogy ◽  
Non Local ◽  
Minimum Uncertainty ◽  
Quantum Hydrodynamic ◽  
Transmission Speed

This work shows that in the frame of the stochastic generalization of the quantum hydrodynamic analogy (QHA) the uncertainty principle is fully compatible with the postulate of finite transmission speed of light and information. The theory shows that the measurement process performed in the large scale classical limit in presence of background noise, cannot have a duration smaller than the time need to the light to travel the distance up to which the quantum non-local interaction extend itself. The product of the minimum measuring time multiplied by the variance of energy fluctuation due to presence of stochastic noise shows to lead to the minimum uncertainty principle. The paper also shows that the uncertainty relations can be also derived if applied to the indetermination of position and momentum of a particle of mass m in a quantum fluctuating environment.

scholarly journals The uncertainty relations and minimum uncertainty states

2003 ◽  
Vol 52 (12) ◽  
pp. 2961
Author(s):  
Deng Wen-Ji ◽  
Xu Yun-Hua ◽  
Liu Ping
Keyword(s):  
Uncertainty Relations ◽  
Minimum Uncertainty

Quantum uncertainty relations and stochastic mechanics

1984 ◽  
Vol 79 (2) ◽  
pp. 175-186 ◽  
Author(s):  
S. De Martino ◽  
S. De Siena
Keyword(s):  
Uncertainty Relations ◽  
Stochastic Mechanics ◽  
Quantum Uncertainty

scholarly journals Uncertainty relations: An operational approach to the error-disturbance tradeoff

Quantum ◽  
2017 ◽  
Vol 1 ◽  
pp. 20 ◽  
Author(s):  
Joseph M. Renes ◽  
Volkher B. Scholz ◽  
Stefan Huber
Keyword(s):  
Quantum Theory ◽  
Uncertainty Relation ◽  
Uncertainty Relations ◽  
Actual Measurement ◽  
Quantum Uncertainty ◽  
Joint Measurability ◽  
Finite Dimensional ◽  
Wave Particle Duality ◽  
Heisenberg Type ◽  
Conceptual Difficulties

The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous measurements, and comparing the values of unmeasured observables is not necessarily meaningful according to quantum theory. To overcome these conceptual difficulties, we take a different approach and define error and disturbance in an operational manner. In particular, we formulate both in terms of the probability that one can successfully distinguish the actual measurement device from the relevant hypothetical ideal by any experimental test whatsoever. This definition itself does not rely on the formalism of quantum theory, avoiding many of the conceptual difficulties of usual definitions. We then derive new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observables of finite-dimensional systems, as well as for the case of position and momentum. Our relations may be directly applied in information processing settings, for example to infer that devices which can faithfully transmit information regarding one observable do not leak any information about conjugate observables to the environment. We also show that Englert's wave-particle duality relation [PRL 77, 2154 (1996)] can be viewed as an error-disturbance uncertainty relation.

Quantum uncertainty relations of Tsallis relative $\alpha$ entropy coherence baed on MUBs

2021 ◽  
Author(s):  
ZHANG Fu Gang
Keyword(s):  
Lower Bound ◽  
Positive Integer ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Mutually Unbiased Bases ◽  
Uncertainty Relations ◽  
Quantum Uncertainty ◽  
Single Qubit ◽  
Qubit System ◽  
Special Case

Abstract In this paper, we discuss quantum uncertainty relations of Tsallis relative $\alpha$ entropy coherence for a single qubit system based on three mutually unbiased bases. For $\alpha\in[\frac{1}{2},1)\cup(1,2]$, the upper and lower bounds of sums of coherence are obtained. However, the above results cannot be verified directly for any $\alpha\in(0,\frac{1}{2})$. Hence, we only consider the special case of $\alpha=\frac{1}{n+1}$, where $n$ is a positive integer, and we obtain the upper and lower bounds. By comparing the upper and lower bounds, we find that the upper bound is equal to the lower bound for the special $\alpha=\frac{1}{2}$, and the differences between the upper and the lower bounds will increase as $\alpha$ increases. Furthermore, we discuss the tendency of the sum of coherence, and find that it has the same tendency with respect to the different $\theta$ or $\varphi$, which is opposite to the uncertainty relations based on the R\'{e}nyi entropy and Tsallis entropy.

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